Amount of time for a half period to occur

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The discussion focuses on calculating the time it takes for a mass-spring system in simple harmonic motion to move from its maximum displacement (x = A) to the equilibrium position (x = 0). The relevant formula for the period (T) is provided, but confusion arises regarding the definition of one cycle and how to apply it to find the half-period. Participants emphasize the importance of understanding the motion through plotting the position function x(t) and recognizing that the amplitude (A) plays a crucial role in the calculations. The conversation highlights the need to clarify the relationship between time and displacement within the context of harmonic motion. Understanding these concepts is essential for correctly solving the problem.
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Homework Statement



A mass-spring system has k = 105 N/m and m = 1.75 kg.

If it is undergoing simple harmonic motion, how much time does it take the mass to go from x = A to x = 0?

Homework Equations



T=2pi*sqrt(m/k)

The Attempt at a Solution



Tried plugging in the values for the equation I gave to find T, then cutting it in half to find the amount of time the question asked for, but it's not the correct answer.
 
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What exactly is one cycle? If you understand that, you'll see why your answer is wrong. It may help to look at a diagram that shows one period in your textbook.
 
When the mass goes into the spring and back?
 
Sketch the x(t) function for a full period and see.

ehild
 
Capncanada said:
When the mass goes into the spring and back?
Yes. So in one cycle, if it starts at x(0)=A, it ends at x(T)=A, but more important, what does x(t) do in between? As ehild suggested, plot x(t) for one cycle.
 
Who's A and can you link it to T ? EDIT: So A's the amplitude...
 
Last edited:
Uhh x goes to A? Which equation can I use to solve for that? x=Acos(ωt)?

Sorry I'm braindead been studying all morning I just want this homework done.
 
Capncanada said:
Which equation can I use to solve for that? x=Acos(ωt)?

Yes. x = A cos (2pi* t/T). How does it look like? What is x at t=0, t=T/8, T/4, ...

ehild
 
So I can plug in x as A so that A cancels out here and then solve for t where T = 1/2?
 
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Capncanada said:
So I can plug in x as A so that A cancels out here and then solve for t where T = 1/2?

Is T=1/2??


Would you please show me a cosine function? Please!

ehild
 
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